{
  "id": "2008.11893",
  "version": "v1",
  "published": "2020-08-27T02:38:46.000Z",
  "updated": "2020-08-27T02:38:46.000Z",
  "title": "Deformation of the scalar curvature and the mean curvature",
  "authors": [
    "Pak Tung Ho",
    "Yen-Chang Huang"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "On a compact manifold $M$ with boundary $\\partial M$, we study the problem of prescribing the scalar curvature in $M$ and the mean curvature on the boundary $\\partial M$ simultaneously. To do this, we introduce the notion of singular metric, which is inspired by the early work of Fischer-Marsden in [18] and Lin-Yuan in [23] for closed manifold. We show that we can prescribe the scalar curvature and the mean curvature simultaneously for generic scalar-flat manifolds with minimal boundary. We also prove some rigidity results for the flat manifolds with totally geodesic boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-27T02:38:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C21"
    ],
    "keywords": [
      "scalar curvature",
      "mean curvature",
      "deformation",
      "generic scalar-flat manifolds",
      "totally geodesic boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}